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Microwave Plasma-Activated Chemical Vapor Deposition of Nitrogen-Doped Diamond. I. N2/H2 and NH3/H2 Plasmas
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Microwave Plasma-Activated Chemical Vapor Deposition of Nitrogen-Doped Diamond. I. N2/H2 and NH3/H2 Plasmas
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School of Chemistry, University of Bristol, Bristol, BS8 1TS United Kingdom
Skobel’tsyn Institute of Nuclear Physics, Moscow State University, Leninskie gory, Moscow 119991, Russia
Institute of Applied Physics, (IAP RAS), 46 Ulyanov st., 603950 Nizhny Novgorod, Russia
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The Journal of Physical Chemistry A

Cite this: J. Phys. Chem. A 2015, 119, 52, 12962–12976
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https://doi.org/10.1021/acs.jpca.5b09077
Published November 23, 2015

Copyright © 2015 American Chemical Society. This publication is licensed under CC-BY.

Abstract

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We report a combined experimental/modeling study of microwave activated dilute N2/H2 and NH3/H2 plasmas as a precursor to diagnosis of the CH4/N2/H2 plasmas used for the chemical vapor deposition (CVD) of N-doped diamond. Absolute column densities of H(n = 2) atoms and NH(X3Σ, v = 0) radicals have been determined by cavity ring down spectroscopy, as a function of height (z) above a molybdenum substrate and of the plasma process conditions, i.e., total gas pressure p, input power P, and the nitrogen/hydrogen atom ratio in the source gas. Optical emission spectroscopy has been used to investigate variations in the relative number densities of H(n = 3) atoms, NH(A3Π) radicals, and N2(C3Πu) molecules as functions of the same process conditions. These experimental data are complemented by 2-D (r, z) coupled kinetic and transport modeling for the same process conditions, which consider variations in both the overall chemistry and plasma parameters, including the electron (Te) and gas (T) temperatures, the electron density (ne), and the plasma power density (Q). Comparisons between experiment and theory allow refinement of prior understanding of N/H plasma-chemical reactivity, and its variation with process conditions and with location within the CVD reactor, and serve to highlight the essential role of metastable N2(A3Σ+u) molecules (formed by electron impact excitation) and their hitherto underappreciated reactivity with H atoms, in converting N2 process gas into reactive NHx (x = 0–3) radical species.

Copyright © 2015 American Chemical Society

1 Introduction

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One of the key classifiers of natural diamonds is their nitrogen impurity content. (1) Nitrogen is the dominant impurity in type I diamonds, where it is typically present at the ∼0.1 atom % level. These constitute ≈98% of all natural diamonds and are traditionally further subdivided according to the way in which the nitrogen impurities are distributed within the carbon lattice (e.g., as isolated atoms, or aggregated as larger clusters), but all exhibit characteristic absorption features in the infrared (IR) and ultraviolet (UV), and visible fluorescence under UV illumination. Type II diamonds contain much lower N impurity levels (too low to be revealed by IR absorption spectroscopy) and are much rarer in nature. Natural type IIa diamonds are both very scarce and particularly prized, as they are almost entirely devoid of impurities and, as a result, are essentially colorless and display the highest thermal conductivity.
In contrast, given minimal air leakage into the reaction chamber and sufficiently pure process gases, diamonds grown by chemical vapor deposition (CVD) can be produced with very low nitrogen content, and are thus normally type IIa material. For example, Tallaire et al. (2) reported single-crystal homoepitaxial growth of diamond with total defect concentrations <200 ppb using high-purity CH4/H2 gas mixtures and a high-power-density microwave (MW) plasma process. These workers also showed that even trace (2–10 ppm) additions of N2 to the CH4/H2 process gas mixture caused a substantial (up to 2.5-fold) increase in growth rate, (2) reinforcing and extending earlier (3) and subsequent (4, 5) studies that demonstrate growth rate enhancements at higher nitrogen atom input mole fraction, X0(N). Careful studies of CVD growth on synthetic (100) high-pressure, high-temperature (HPHT) single-crystal diamond substrates by Achard et al. (6) served to illustrate not just the evolution in growth mechanism, from a unidimensional (step flow) to a bidimensional nucleation mode, upon increasing X0(N), but also the interdependence of diamond deposition rate, growth mechanism (hence morphology), and substrate temperature.
Here we report the first in a sequence of studies designed to provide an in-depth analysis and understanding of the roles of nitrogen in diamond CVD. The presence of nitrogen in MW-activated CH4/H2 plasmas can be traced by optical emission spectroscopy (OES). Several previous studies have reported the variation in CN(B–X) emission intensity upon varying X0(N) in CH4/H2 plasmas, (3, 7, 8) but quantifying the CN number density is much harder, and it remains to be established what measurements of relative CN emission intensities (normally from the plasma core) tell one about the densities of the various different N-containing species near the growing diamond surface.
This question will be addressed in a future publication (paper II), via spatially resolved absolute and relative density measurements of H(n = 2, 3) atoms, CH, NH, C2, and CN radicals, and metastable triplet N2 molecules in MW-activated CH4/N2/H2 gas mixtures, using a combination of absorption (cavity ring down) spectroscopy (CRDS) and OES. (9) These data will be discussed and interpreted in light of complementary two-dimensional (2-D (r, z), where r and z are, respectively, the radial distance and the vertical height from the center of the substrate surface) modeling (10) of the C/N/H plasma chemistry and composition as a function of process conditions, i.e., CH4 and N2 fractions, total pressure p, and applied MW power P. Such analysis returns absolute number density estimates for the more abundant N-containing radical species, such as NHx (x = 0–2) and CN radicals, in the immediate vicinity of a growing diamond surface. The results can then be used to inform models of elementary reaction sequences, whereby such species can add to, and migrate on, a diamond (100) surface, as modeled using a mixture of quantum and molecular mechanical (QM and QM/MM) methods. This gas–surface chemistry modeling work will form the basis of a future third paper in this series (paper III). (11)
The present paper (paper I) reports spatially resolved absorption and/or emission measurements of H(n = 2, 3) atoms, NH radicals, and triplet N2 molecules in MW-activated N2/H2 and NH3/H2 plasmas operating at pressures (∼150 Torr) and powers (∼1.5 kW) relevant to commercial MW plasma-activated (PA) CVD reactors. These results inform and tension companion 2-D modeling of the N/H plasma chemistry, and represent an essential precursor to the detailed analysis of MW-activated C/N/H plasmas reported in paper II. N2/H2 plasmas have been studied previously, in low-pressure direct current (dc) (12) and MW (13) discharges, and at higher pressures in an expanding arc reactor, (14, 15) but we are not aware of any quantitative investigations at the conditions of pressure, temperature, and electron density normally prevailing in MWPACVD reactors used for diamond growth.

2 Experimental Methods

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The MWPACVD reactor, the laser system, and the optical arrangements for the spatially resolved CRDS measurements as a function of height (z) above the substrate surface have been described elsewhere. (16) CRDS was used to determine absolute column densities of electronically excited H(n = 2) atoms (monitoring the n = 3 ← n = 2 Balmer-α transition) (17) and ground state NH(X3Σ, v = 0) radicals (using selected lines within the A3Π–X3Σ system, as in our previous study of hot filament-activated NH3-containing C/N/H gas mixtures). (18) The previously described optical setup for OES measurements (19) was revised for the present work, with a simple Keplerian telescope arrangement providing greatly enhanced light-gathering ability relative to the prior approach. With the trade-off of spatial resolution (now ≈3 mm) for improved spectral resolution (now 0.15 nm fwhm) and signal-to-noise ratio, partially rotationally resolved UV emission spectra were obtained that show detailed (but strongly overlapped) rovibronic structure due to N2 and NH (and, in the case of C/N/H plasmas, also CN and CH) radicals, as described below. The N2 and NH OES data reported here and in paper II were all taken with the spectrometer transmission centered at ≈336 nm. Though not important for N/H plasmas, this choice is crucial in the case of C/N/H plasmas since it avoids the much stronger CN, CH, and C2 emissions lying further to the red, which would otherwise limit the maximum possible integration time before detector saturation and thus render our measurements insufficiently sensitive toward N2 and NH. An important difference with respect to the previous configuration (19) is that the present OES measurements are sampled from a volume nominally at the radial center of the plasma, rather than attempting to emulate the line-integrated sampling mode of CRDS.
The H2, N2, and NH3 source gases were introduced through separate, calibrated mass flow controllers (MFCs), and mixed prior to entering the reactor through two diametrically opposed inlets located close below the fused silica window (which constitutes the top of the reactor), at an angle of ≈45° to the probe axis. “Base” conditions for the experimental studies were defined as follows: total pressure p = 150 Torr, input power P = 1.5 kW, and input flow rates F(N2) = 3 standard cm3 per minute (sccm) for OES measurements or 6 sccm for CRDS, F(NH3) = 6 sccm, and F(H2) = 500 sccm. When one parameter was varied, all others were maintained at their base values, except where noted. The substrate temperature Tsub was monitored using a two-color optical pyrometer operating in the wavelength range 700–1000 nm, which indicated a higher value (≈1100 K) under base conditions than the ≈973 K estimated by one-color pyrometry as used in our previous work. (10) We consider the new value more reliable due to its independence of an (usually problematic) estimate of substrate emissivity, which is itself a function of temperature as well as sensitively dependent on surface condition.

3 Experimental Results

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Figure 1a shows a CRDS measurement of a small part of the NH(A3Π–X3Σ) Δv = 0 band system obtained at z = 8 mm from a N2/H2 plasma operating under base conditions. Given literature values for the relevant spectroscopic constants (20) and Franck–Condon factors, (21, 22) a simulation (as shown in the figure) can be constructed using PGOPHER (23) that provides assignments for rotational lines originating from the v″ = 0 and v″ = 1 vibrational levels, and which may be fitted to the experimental spectrum to recover absolute column densities. Both the fitted simulation and that of the complete NH(A–X) Δv = 0 progression, shown in Figure 1b, assume rotational and vibrational temperatures (Trot and Tvib) of 2900 K.

Figure 1

Figure 1. Part of the NH(A–X) Δv = 0 band system (a) as measured by CRDS at z = 8 mm in a N2/H2 (6/500 sccm) plasma operating under base conditions, with fitted PGOPHER simulation at fixed Trot = Tvib = 2900 K, and (b) shown in the context of the complete (simulated) progression, illustrating the overlapping v′–v″ = 0–0, 1–1, and 2–2 bands.

The optical emission spectrum displayed in Figure 2a spans a much wider (≈50 nm) wavelength range, and reveals not just the NH(A–X) Δv = 0 band system at ≈336 nm, but also progressions of vibronic bands associated with the second positive (C3Πu–B3Πg) system of N2. (24, 25)Figure 2b,c shows expanded views of parts of this system. The former shows the N2(C–B) Δv = −1 and Δv = −2 progressions along with a PGOPHER simulation using the appropriate spectroscopic constants, (24) while the latter illustrates the separation of the overlapping N2(C–B) (0,0) band and NH(A–X) Δv = 0 progression, which must be accomplished with high fidelity (26) in order to track the variation in emission intensity for each species with z and/or process conditions. For brevity, the N2(C–B) (0,0) and NH(A–X) (0,0) band emissions, the intensities of which we consider representative and report exclusively in the remainder of this work, will henceforth be referred to simply as N2* and NH*. Spectra recorded at longer wavelengths showed the usual intense H Balmer series emission (19) (henceforth H*), but no detectable emissions from atomic nitrogen, even when X0(N) was raised to 30%. The various multiplets associated with the 2p23p1 → 2p23s1 transition of N lying near 744, 820, and 865 nm all possess large A-coefficients (≈107 s–1) (27-29) and occur in a wavelength range for which our detection is relatively more sensitive than in the UV. Thus, they should be readily observable if the N(2p23p1) densities were comparable to those of the other species, but this is far from the case. (30)

Figure 2

Figure 2. Optical emission spectra, measured at z = 7 mm, of a MW-activated N2/H2 (9/500 sccm) mixture operating otherwise under base conditions. (a) Overview spectrum showing the NH(A–X) Δv = 0 band system centered at ≈336 nm, along with three progressions of bands from the second positive (C3Πu–B3Πg) system of N2. Panel (b) shows an expanded view of the N2(C–B) Δv = −1 and Δv = −2 progressions, while part (c) illustrates the overlapping N2(C–B) 0–0 band and NH(A–X) Δv = 0 progression. Both are shown together with a common PGOPHER simulation, vertically offset for clarity in part (b), using the appropriate spectroscopic constants and with respective rotational temperatures treated as parameters and varied for best fit.

OES is a valuable technique for determining variations in relative species concentration with changes in process parameters, providing that the latter changes have minimal confounding influence on that part of the electron energy distribution responsible for exciting the optical emission. CRDS, in contrast, provides absolute column densities. The procedure for obtaining H(n = 2) column densities from CRDS measurements on the n = 3 ← n = 2 Balmer-α transition is unchanged from that used in our previous studies, (16) and so is not repeated here. The experimental measurable is the change in ring down rate (Δk, s–1) versus wavenumber (ν̅, cm–1). For a radical species such as NH, eq 1 provides the link from CRDS measurements of an individual spectral line to the absolute column density, which we notate as, e.g., {NH(v = 0)}:(1)Here, L is the length of the cavity (92 cm), gl and gu are the degeneracies of the X3Σ and A3Π states (3 and 6, respectively), and A is the Einstein A-coefficient for the (0,0) band of the A–X transition. In the present work, A has been taken as ≈2.44 × 106 s–1 per ref 21, although it should be noted that other similar values have been given in the more recent ref 22 and references therein. pline is the ratio of the integrated intensity of the spectral line under study to the total band intensity, which is calculated assuming that the NH radicals are localized in a volume of reasonably constant gas temperature, T. Given the collision frequency at the pressures of interest, and informed by rotational temperatures obtained by fitting to the observed band contour of the NH* optical emission spectrum, we assume Tgas = Trot = T = 2900 ± 300 K, and hence calculate pline using PGOPHER and the relevant spectroscopic constants, (20, 21) with the total band intensity obtained as the integrated intensity over all rotational lines within the (0,0) band. The calculated pline values for the lines contributing to the simulation shown in Figure 1 are 5.44(12) × 10–3, 4.81(11) × 10–3, and 1.07(7) × 10–3 for the (0,0) pP1(10) (29 466.02 cm–1), (0,0) qP32(9) (29 471.65 cm–1), and (1,1) pP1(7) (29 471.80 cm–1) lines, respectively, where the quoted uncertainties are due to the range of T considered. Given the experimental resolution (≈0.3 cm–1 fwhm), the latter two lines are unresolved, and line-integrated Δk values were obtained by simultaneously fitting one (assumed Gaussian) profile to the pP1(10) line, and another of equal width to the sum of the other two lines, with the relative area of the latter fixed to its temperature-determined value of 0.925(15). From these three lines we hence recovered “pP1(10)-equivalent” values of Δk, from which column densities were calculated using the corresponding pline. The choice of lines was guided partly by the uncertainty in temperature, and thus minimal variation of the relative intensities was sought: the values of pline and the intensity ratio, even including implausibly high (3600 K) and low (2200 K) average temperatures, span the fairly narrow ranges 5.02 × 10–3–5.74 × 10–3 and 0.884–0.980, respectively, for the lines used in the present analysis.
Figure 3a,b shows z-dependent profiles for {H(n = 2)} and {NH(v = 0)} as measured by CRDS in N2/H2 and NH3/H2 plasmas, respectively, operating under base conditions. The {H(n = 2)} profiles in these dilute N/H plasmas appear insensitive to the choice of nitrogen precursor, and are reminiscent of those reported previously when using dilute C/H/(Ar) (16) and C/H/O (17) gas mixtures in this same reactor, peaking at z ≈ 6 mm and decreasing both toward the substrate and (less steeply) at larger z. The {NH(v = 0)} distribution is clearly more extensive in both cases, and the measured {NH(v = 0)} values in the two plasmas are very similar despite the approximately 2-fold difference in X0(N) between the two precursor gases for any given flow rate.

Figure 3

Figure 3. Profiles of {NH(v = 0)} (black circles) and {H(n = 2)} (red triangles) with respect to z obtained by CRDS probing of (a) N2/H2 (6/500 sccm, filled symbols) and (b) NH3/H2 (6/500 sccm, open symbols) plasmas operating under base conditions. The gray and orange lines are calculated {NH(v = 0)} and {H(n = 2)} profiles, respectively.

Figure 4 shows measured variations in {H(n = 2)} and {NH(v = 0)} at z = 8 mm with changing X0(N) for (a) N2/H2 and (b) NH3/H2 plasmas. The results are presented with respect to N/H atom ratio, defined in terms of the flow rates as F(N2)/F(H2) and F(NH3)/[3F(NH3) + 2F(H2)], respectively, depending on the N precursor. We further note that X0(N) and the N/H atom ratio are almost equal for small nitrogen additions. {H(n = 2)} appears insensitive to small additions of N2 or NH3, while {NH(v = 0)}, unsurprisingly, increases with X0(N). The rate of increase is less than directly proportional in both cases, with the rate of rise diminishing as X0(N) further increases. A sharp rise of {NH(v = 0)} for F(NH3) < 1 sccm can be inferred from the zero-offset observed in Figure 4b, which contrasts with the roughly linear trend seen for small F(N2). The continuous curves drawn through the data points are power laws of the form const × X0(N)a, with best-fitting exponents (a) a = 0.70 and (b) a = 0.36. We discuss the interpretation of these values in the following section.

Figure 4

Figure 4. Variations in {H(n = 2)} and {NH(v = 0)} for (a) N2/H2 and (b) NH3/H2 plasmas plotted as a function of N/H ratio in the input gas mixture (defined on the top and bottom horizontal axes, respectively). Both plasmas operated otherwise at base conditions and were probed at z = 8 mm. The symbol key is as in Figure 3. The black lines are curves of the form {NH(v = 0)} ∼ X0(N)a, with best-fitting exponents of (a) a = 0.70 and (b) a = 0.36. The gray squares and orange diamonds show calculated values of {NH(v = 0)} and {H(n = 2)}, respectively, under the given conditions. The calculated {NH(v = 0)} values for the NH3/H2 plasma (not shown) are roughly twice the experimental values, as discussed in the text.

Column density variations with power and pressure, again measured at z = 8 mm, with all other parameters maintained at their base values, are shown in Figure 5. The {NH(v = 0)} versus P plot, Figure 5a, clearly demonstrates sensitivity to the choice of nitrogen precursor. In the case of the N2/H2 plasma, {NH(v = 0)} increases approximately 4-fold as P is raised from 0.8 to 1.8 kW, whereas the same increase in P in the case of NH3/H2 leads to a modest reduction in {NH(v = 0)}. The value of {NH(v = 0)} is, however, consistently greater in the NH3/H2 plasma for all powers, even though X0(N) is only one-quarter of that for the corresponding N2/H2 plasma. Changes in pressure have an effect roughly analogous to those of power: as seen in Figure 5b, {NH(v = 0)} largely follows {H(n = 2)} in the N2/H2 mixture, but shows only weak dependency on either variable when using NH3 as the N source gas. We emphasize, however, that the trends shown in Figure 5 reflect the changing size and power density of the plasmas as well as their local compositions and parameters, so that physical interpretation must necessarily rely in large part on the complementary modeling studies.

Figure 5

Figure 5. Variations in {H(n = 2)} and {NH(v = 0)}, probed at z = 8 mm, with respect to (a) applied MW power and (b) pressure. The plasmas were maintained otherwise at base conditions, with flows of 6/500 sccm for both the N2/H2 and NH3/H2 mixtures. The symbol key is as in Figure 4, with filled and open symbols for the N2/H2 and NH3/H2 plasmas, respectively. Points in each series are joined by straight line segments for visual clarity. Calculated {H(n = 2)) and {NH(v = 0)} values are again indicated with orange diamonds and gray squares, respectively, and the latter values for the NH3/H2 plasma are off scale and thus not shown.

OES measurements show many of the same trends. Spatial profiles of the H* emission from the N2/H2 and NH3/H2 plasmas (Figures 6a,b), respectively) are very similar to each other and, peaking at z ≈ 6 mm, have overall envelopes comparable to those given in Figure 3 for {H(n = 2)} as measured by CRDS. The N2* emission spatial profile closely resembles that of H*. It should be noted that the relative emission intensities given for z = 0 mm are consistently and necessarily underestimates relative to the other spatial locations, since the substrate (rather than the plasma) then fills the lower half of the imaged region; CRDS measurements, in contrast, are impossible with the substrate partially occluding the beam path. The shapes of the NH* emission profiles are insensitive to the choice of nitrogen source, but peak at larger z than the H* profiles, which is again consistent with the CRDS measurements of {NH(v = 0)}. In both plasmas, the NH*/N2* emission ratio increases approximately 2-fold across the range z = 0 to 18 mm, reflecting this more extensive NH distribution.

Figure 6

Figure 6. z-profiles of H*, NH*, and N2* emissions from (a) N2/H2 (3/500 sccm) and (b) NH3/H2 (6/500 sccm) plasmas, both operating under base conditions. The emission intensities displayed in both panels are mutually normalized, for each species, to the maximal value measured at any z from either plasma. The symbol key is as in the previous figures, with the addition of blue diamonds for N2*. The orange lines show calculated H(n = 3) (relative) concentrations at r = 0 as a function of z for the respective plasmas, and match well with the measured H* emission profiles. The points in the NH* and N2* profiles are joined with straight line segments for visual clarity.

The measured NH* emission from the NH3/H2 plasma is more intense than that from the equivalent N2/H2 plasma. So, too, is the N2* emission. The former observation may be explained, at least partially, by the finding from CRDS that the (ground state) NH density is greater for NH3 additions than with the same X0(N) from N2, but the latter also implies some contribution from increased electron density ne and/or temperature Te in the NH3/H2 case. This finding is illustrated more clearly in Figure 7, which shows the scaling of the emission intensities with N/H atom ratio for both plasmas. The H* emission shows a small, but sharp, increase upon small additions of NH3, and a similar but more gradual increase when using N2, while no comparable effect was seen for {H(n = 2)} in Figure 4a; any differences in the N2* emission intensities are hard to discern. The small increases in H* and the linear increase in N2* emission intensity imply that increasing X0(N) in the source gas mixture causes only minor variations in the plasma parameters. Such variations as are observed could reflect changes in the dominant ion(s) and in electron–ion recombination rates and/or minor changes of the maximum gas temperature Tmax and Te. We return to this issue in section 4, but the similar N2* emission intensities, and the fact that this quantity scales essentially directly proportionally to the input N/H atom ratio, both suggest that the strongly bound N2 molecule is the predominant reservoir for nitrogen in both plasmas. Similarly to {NH(v = 0)}, the NH* emission intensity exhibits an approximate power-law relationship to X0(N), again with a smaller exponent (a = 0.47) for the NH3/H2 mixture than for N2/H2 (a = 0.81).

Figure 7

Figure 7. H*, NH*, and N2* emission intensities measured at z = 7 mm for N2/H2 (filled symbols) and NH3/H2 (open symbols) plasmas, both operating under otherwise base conditions, plotted as a function of N/H ratio in the input gas mixture. Symbols are as in Figure 6. Emission intensities are normalized to the maximum value observed for each species, and flow rates of the respective nitrogen precursors are expressed as N/H atom ratios. The black lines are curves of the form NH* ∼ X0(N)a, with best-fitting exponents of a = 0.81 in the N2/H2 case and a = 0.47 for NH3/H2.

The N2* and NH* emissions from N2/H2 and NH3/H2 plasmas respond similarly to changes in applied microwave power as do {H(n = 2)} and {NH(v = 0)}, as may be seen by comparing the relevant data in Figures 8a and 5a. One notable observation is that the N2* emission intensity increases less steeply with P than does {H(n = 2)}, despite the H(n = 2) energy (with respect to ground state H) being a little below that of N2(C3Πu) with respect to its ground state, i.e., 10.2 and 11.0 eV, respectively. Further discussion and interpretation of these various observations draws on companion modeling studies of the plasma chemistry and composition which are described below.

Figure 8

Figure 8. NH* and N2* emission intensities measured (a) at z = 7 mm (N2/H2 plasma, 3/500 sccm, filled symbols) and z = 5 mm (NH3/H2 plasma, 6/500 sccm, open symbols) as a function of P and (b) at z = 5 mm for N2/H2 (3/500 sccm) and NH3/H2 (6/500 sccm) plasmas (filled and open symbols, respectively) as a function of p. All other parameters were maintained at their base values, and the emission intensities for each species are mutually normalized to the maximal value measured at any P, in panel (a), or p, in panel (b), from either plasma. Calculated values of the (relative) N2(C ← X) and NH(A ← X) EI excitation rates are shown as pale blue triangles and gray squares, respectively.

4 N/H Plasma Modeling

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Our description of the N/H plasma modeling starts by highlighting similarities (with regard to both processes and effects) associated with adding small amounts of N2 or NH3 (up to a few percent) to a H2 plasma. For both N source gases, the 2-D model (elaborated below) shows N2 molecules to be the dominant N-containing species, representing ≈99.99% (N2/H2) and ≈92% (NH3/H2) of the total nitrogen content in the reactor under “base” conditions of power P = 1.5 kW, pressure p = 150 Torr, and input mole fraction X0(N2 or NH3) = 1.2%. The N/H plasma-chemical kinetics and species concentrations in the hot plasma region thus share many common features. However, it is important to recognize a significant difference in the case of the NH3/H2 gas mixture: the additional source of NHx (x = 0–2) species resulting from NH3 diffusion from the peripheral, cold regions of the reactor (primarily near the gas inlets) into the central hot plasma region.
Addition of either N-containing gas leads to a similar change in the dominant ions, from H3+ in the case of the pure H2 plasma, to a mix of NH4+ and N2H+ ions in a N/H plasma operating at base conditions. With 1.2% addition of either N2 or NH3 precursor, [H3+] is reduced to less than 0.3% of ([NH4+] + [N2H+]). We note, however, that the “pure” H2 plasmas used in the present experiments for measurements with no deliberately added N-containing gas will still contain trace amounts of air (i.e., N2 and O2). Assuming, as in our previous studies of MW-activated B/H plasmas, (31) a worst-case scenario of 50 ppm air impurity (containing 40 ppm of N2 and 10 ppm of O2), H3+ would already have been supplanted as the dominant ion by a mixture of H3O+, N2H+, and NH4+ ions with total concentration ≈1011 cm–3 and associated ion–electron recombination coefficients β ≈ (0.5–2) × 10–8 cm3 s–1. In practice, therefore, the ionization–recombination balance associated with the charged particles and the resulting plasma parameters (electron temperature Te and density ne) will be perturbed little by small additions of N2 or NH3. This expectation is consistent with the small increase in Hα emission (Figure 7) and the lack of any discernible jump in the Hα absorption measurements (Figure 4), and stands in marked contrast to the previously reported >100% increase in Hα emission and {H(n = 2)} when adding CxHy to a H2 plasma. (10, 16, 19) In the case of an N2/H2 plasma, N2H+ is progressively supplanted as a major ion by NH4+ upon increasing F(N2) as a result of the reaction N2H+ + NH3 → NH4+ + N2.
The N/H thermochemistry and plasma-chemical mechanism used in the present study were developed on the basis of GRI-Mech 3.0 for H, H2, N2, and NHx (x = 0–3), (32) expanded to involve (i) N2Hx (x = 1–4) species (33, 34) and (ii) plasma chemistry for charged species and excited states involved in various ion conversion and electron–ion recombination reactions. (35, 36) Also considered were species ionization, excitation of rovibrational states H2(v, J), and electron impact (EI) excitations forming H(n = 2, 3), an “effective” excited state of molecular hydrogen with Ei > 11 eV (H2*), and N2*. As before, (10) rate coefficients for processes within block (ii) and their dependence on the local electron energy distribution function (EEDF) and reduced electric field (E/N, where N is the total number density) were estimated using a 0-D framework, wherein the kinetic equations for the EEDF and the local balance equations describing the plasma-chemical kinetics for the charged and neutral species were solved consistently for the range of E/N and T values of interest. Extensive chemical database analysis and test 2-D model calculations assuming various chemical schemes for the additional blocks (i) and (ii) result in the core N/H reaction mechanism presented in Table 1 (where some reactions found to be unimportant under any conditions relevant to the present work have been omitted for brevity).
Table 1. N/H Chemical Mechanism Used in the Present Study with the T- and Te-Dependent Rate Coefficients k (cm3 mol–1 s–1)a
 rate coefficient k = ATb exp(−E/RT)  
reactionAbERforward/(cm–3 s)Rreverse/(cm–3 s)
H + H + H2 ⇌ H2 + H29.00 × 1016–0.601.179 × 10181.354 × 1019
H + H + H ⇌ H2 + H1.00 × 1018–104.042 × 10164.641 × 1017
NH3 + H ⇌ NH2 + H25.40 × 1052.499151.409 × 10181.410 × 1018
NH2 + H ⇌ NH + H24.00 × 1013036504.379 × 10174.390 × 1017
NH + H ⇌ N + H21.88 × 1081.552057.205 × 10177.206 × 1017
N + NH ⇌ N2 + H3.00 × 1013005.094 × 10125.655 × 1011
N + NH2 ⇌ N2 + H + H7.26 × 1013001.481 × 10131.436 × 1011
N + NH2 ⇌ N2H + H1.00 × 1013002.039 × 10122.277 × 1011
NH + NH ⇌ N2 + H + H5.10 × 1013007.523 × 10127.277 × 1010
NH + NH ⇌ N2H + H8.00 × 10110.519874.478 × 10124.989 × 1011
NH + NH2 ⇌ N2H2 + H4.27 × 1014–0.272–778.784 × 10123.406 × 1012
NH2 + NH2 ⇌ N2H2 + H21.70 × 1081.62117831.861 × 10127.234 × 1011
NH2 + NH3 ⇌ N2H4 + H193.11501151.303 × 1083.458 × 107
N2H4 + H ⇌ N2H3 + H24.54 × 1071.826136.459 × 1089.143 × 108
N2H3 + H ⇌ N2H2 + H22.40 × 1081.5–108.725 × 1099.042 × 109
N2H2 + H ⇌ N2H + H23.60 × 1081.5817178.158 × 10122.350 × 1012
N2H + H ⇌ N2 + H23.60 × 1081.5817173.673 × 10153.662 × 1015
NH2 + NH2 ⇌ NH + NH35.6163.535551.770 × 10121.773 × 1012
NH + M ⇌ N + H + M2.65 × 1014075 5001.156 × 10141.007 × 1013
NH2 + M ⇌ NH + H + M3.16 × 1023–291 4001.241 × 10151.084 × 1014
NH3 + M ⇌ NH2 + H + M2.20 × 1016093 4681.770 × 10151.544 × 1014
N2H2 + M ⇌ N2H + H + M1.90 × 1027–3.566 1077.238 × 10111.816 × 1010
NH + N ⇌ N2(A3) + H4.50 × 1010007.641 × 1091.233 × 1014
N2(A3) + H ⇌ N2 + H1.26 × 1014002.538 × 10161.746 × 1011
N2(A3) + H2 ⇌ N2 + H + H5.00 × 1012044506.203 × 10153.717 × 109
N2(A3) + NH3 ⇌ NH2 + H + N27.47 × 1013005.475 × 10113.284 × 105
N + N + H2 ⇌ N2(A3) + H25.00 × 10130–9979.008 × 1061.669 × 1012
N + N + N2 ⇌ N2(A3) + N23.00 × 10140–9971.701 × 1053.152 × 1010
H(n = 3) → H(n = 2) + 4.40 × 107002.766 × 1014 
H(n = 2) → H + 4.70 × 108002.956 × 1016 
H(n = 3) → H + 5.50 × 107003.457 × 1014 
H2* → H2 + 2.00 × 107003.317 × 1016 
H2(v = 1) + H → H2(v = 0) + H1.26 × 1091.3522001.210 × 1023 
H2(v = 0) + H → H2(v = 1) + H1.26 × 1091.3514 0891.208 × 1023 
H2(v = 1) + H2 → H2(v = 0) + H21.88 × 1071.595502.213 × 1022 
H2(v = 0) + H2 → H2(v = 1) + H21.88 × 1071.521 4392.210 × 1022 
H(n = 2) + H2 → H + H + H1.00 × 1013004.872 × 1014 
H(n = 3) + H2 → H + H + H1.00 × 1013004.869 × 1013 
H(n = 2) + H2 → H3+ + e1.00 × 1013016 1302.914 × 1013 
H(n = 3) + H2 → H3+ + e1.00 × 1013004.869 × 1013 
H2+ + H2 → H3+ + H1.20 × 1015003.242 × 1014 
H2+ + N2 → N2H+ + H1.20 × 1015001.021 × 1012 
H3+ + N2 → N2H+ + H21.08 × 1015005.663 × 1014 
H3+ + NH3 → NH4+ + H21.63 × 1015007.330 × 1011 
H+ + H2 + H2 → H3+ + H23.60 × 1019–0.501.651 × 1014 
N2+ + H2 → N2H+ + H1.20 × 1015001.303 × 1012 
N2H+ + NH3 → NH4+ + N21.38 × 1015003.081 × 1014 
NH3+ + H2 → NH4+ + H1.20 × 1012003.560 × 1011 
 rate constant k = ATeb exp(−E/(RTe)) 
electron reactionsAbE 
H(n = 2) + e → H(n = 3) + e2.53 × 1016043 7751.059 × 1011
H(n = 3) + e → H(n = 2) + e3.10 × 1016006.220 × 1010
H + e → H(n = 2) + e1.21 × 10160235 0012.980 × 1016
H(n = 2) + e → H + e1.17 × 1016002.348 × 1011
H + e → H(n = 3) + e1.39 × 10150278 5457.197 × 1014
H2(v = 0) + e → H2(v = 1) + e2.00 × 1015011 9801.725 × 1020
H2(v = 1) + e → H2(v = 0) + e2.30 × 1015003.826 × 1019
H2 + e → H + H + e2.43 × 10150191 2263.841 × 1017
H2 + e → H + H + e8.88 × 10150267 2609.203 × 1016
H2 + e → H2* + e3.20 × 10150267 2603.317 × 1016
H2* + e → H2 + e1.00 × 1015005.302 × 1011
N2 + e → N + N + e5.12 × 10140282 2319.772 × 1012
N2 + e → N + N + e1.87 × 10150287 9912.900 × 1013
NH3 + e → NH2 + H + e1.20 × 10160184 0006.667 × 1012
NH2 + e → NH + H + e1.20 × 10160184 0001.884 × 1012
N2 + e → N2(A3) + e1.10 × 10160142 1533.171 × 1016
H2* + e → H2+ + e + e4.84 × 1015088 2411.087 × 1011
H + e → H+ + e + e1.11 × 10150313 3301.651 × 1014
H2 + e → H2+ + e + e7.23 × 10140354 8103.251 × 1014
N2 + e → N2+ + e + e1.09 × 10150359 4131.303 × 1012
NH3 + e → NH3+ + e + e6.81 × 10150249 9763.560 × 1011
H2+ + e → H(n = 2) + H5.00 × 1018–0.6709.277 × 108
H3+ + e → H2 + H(n = 2)2.89 × 1014001.980 × 1010
N2H+ + e → N2 + H2.50 × 1019–0.901.569 × 1014
NH4+ + e → NH3 + H3.00 × 1018–0.6701.375 × 1014
NH4+ + e → NH2 + H + H3.00 × 1018–0.6701.375 × 1014
a

N2(A3) represents the metastable A3Σu+ state (the lowest energy triplet state) of N2. The last two columns show the forward and reverse reaction rates calculated in the core (i.e., r = 0, z = 10.5 mm) of a 1.2% N2/H2 plasma with T = 2882 K and Te = 1.21 eV (14 042 K), for P = 1.5 kW and p = 150 Torr. Units: cal, cm, s, K, R = 1.987 262 cal (mol K)−1, M is a third body, and the gas temperature T and electron temperature Te are quoted in K.

As in our previous analyses of activated C/H and N/H gas mixtures, (10, 18) fast H-shifting reactions establish the concentration distributions of N1Hx (x = 0–3) and N2Hx (x = 0–4) species. However, these are sensitive not only to the local gas temperature and [H]/[H2] ratio, but also to transport processes (diffusion, thermodiffusion, and flow transfer) and gas–surface reactions at the substrate, the substrate holder, the quartz window, and the reactor walls. The less stable N2Hx (x = 1–4) species survive only in the cold, near-wall regions. The most problematic parts of the mechanism are the less-well-established exchange processes between the N1Hx and N2Hx families, which could involve contributions from both heterogeneous reactions and reactions involving excited species (e.g., N2*), as discussed below.

4.1 N2/H2 and NH3/H2 Plasma Activation and Dependences on X0(N)

4.1.1 N2/H2 Mixtures

The present analysis of the N/H chemistry in MWCVD reactors starts with the simpler N2/H2 gas mixtures, wherein nitrogen species conversion begins with dissociation of N2. The ground state N2(X1Σ+g) molecule, henceforth identified as simply N2, has a high bond strength: D0(N≡N) = 9.78 eV. Thus, the first issue to address is the dominant N2 dissociation mechanism under typical plasma conditions of Te ≈ 1.1–1.3 eV and (r, z) distributions of gas temperature T and electron density ne as in Figure 9. The obvious inhomogeneity of these distributions serves to illustrate some of the challenges to reproducing and interpreting experimental CRDS and OES data.

Figure 9

Figure 9. Two-dimensional (r, z) distributions of gas temperature T and electron concentration ne for base conditions and 1.2% N2/H2 mixture. The model assumes cylindrical symmetry, a substrate diameter of 3 cm, and a reactor radius, Rr = 6 cm, and height, h = 6.2 cm.

Two-dimensional model runs with the available N/H chemistry rule out a purely thermal mechanism given prevailing gas temperatures T < 3000 K: reactions involving ground state neutral species (e.g., N2 + H → NH + N) simply do not provide sufficient activation, and calculations on this basis return NH column densities that are orders of magnitude lower than the measured {NH(v = 0)} as given in Figures 3 and 4. We note that previously proposed wall reactions (14, 15) are also unable to provide NH densities comparable to those observed. Given the calculated EEDF, we estimate a rate coefficient, k1,diss < 5 × 10−13 cm3 s–1, for N2 dissociation by EI:(1)Reaction 1 is thus a relatively more important N2 dissociation route, but still fails (by an order of magnitude) to support the measured NH column densities. Other suggested dissociation mechanisms in N2 plasmas, involving electronically excited N2* and vibrationally excited N2(v ≥ 14) molecules, (37) are also unimportant in the present case.
Seeking other possible N2 dissociation mechanisms, we considered excited states of N2, and particularly its lowest, metastable A3Σ+u state, henceforth denoted as N2(A3). This has an excitation threshold ε = 6.2 eV, and higher triplet states, including the C and B states involved in the N2* OES spectrum, can also decay (radiatively and/or collisionally) to N2(A3). Thus, N2(A3) has been included in the kinetic scheme (Table 1) and an excitation rate coefficient k2 for the process(2)calculated from the EEDF, with additional contributions to account for cascades from higher triplet states of N2. Typical values of k2 for the present MW plasma conditions are k2[cm3 s–1] = 1.8 × 10–8 × exp(−6.2/Te[eV]). From the perspective of dissociating N2, the most effective way to use this electronic excitation appears to be through the spin-allowed reaction 3 with H atoms, which is the most populous radical in the present study, with typical mole fractions X(H) ≈ 5–10% in the plasma core. That is(3)with rate coefficient k3 yet to be determined. One fast discharge flow study (38) concluded that reaction 3 is improbable, but careful inspection of that data allows an alternative interpretation that is compatible with the kinetics proposed here. The prior conclusion was based on an observation that H atom addition to a N2(A3)/H2 mixture caused no discernible increase in measured NH. Our simulations of the earlier experimental conditions suggest that the NH concentration would actually increase at early reaction times by reaction 3, but then decline (due to the reaction NH + H → N + H2) in contrast to the steady growth in [NH] observed in experiments with no added H atoms. Assuming k3 < 2.8 × 10–15 cm3 s–1 at T = 295 K (the temperature of the fast discharge flow experiment), the predicted NH concentration at the time of measurement, t = 14 ms, is indeed lower than with no added H atoms, which is consistent with the prior observation. More detailed discussion and reinterpretation of the earlier experimental results is reserved for the Appendix.
The proposed source of NHx through reaction 3 will, however, be reduced by competition with the fast deactivation of N2(A3) through collision with H and H2:(4)(5)
The evaluation by Herron (39) recommends rate coefficients k4 = 2.1 × 10–10 cm3 s–1 and k5(298 K) ≈ (4 ± 2) × 10–15 cm3 s–1, while Slanger et al. (40) have k5(T) = 2.2 × 10–10 exp(−3500/T) over the limited temperature range 240 < T < 370 K. The present MWCVD model requires k5(T), as well as k3(T), over the much wider temperature range 300 < T < 3000 K. Given typical values of XH ≈ 5–10% in the plasma region, reaction 4 will be the dominant quenching reaction provided that k5 shows only a limited increase with T, i.e., if k5 < 5 × 10–12 cm3 s–1 at T = 3000 K. For determinacy, we have assumed this condition and hence set k5(T) = 8.3 × 10–12 exp(−2239/T), which reproduces both the Slanger et al. measurements (40) at T = 370 K and Herron’s recommended value (39) of k5(298 K). A consequence of this assumption, however, is that the k3(T) values that we now deduce for the plasma core region (at T ≈ 2500–3000 K) should be regarded as lower bounds. Proceeding as such, we note that the rate coefficient for NH + N → N2 + H is temperature-independent (k = 5 × 10–11 cm3 s–1, cf., Table 1), and have taken k–3 to be similarly independent of temperature. Combining an assumed value of k–3 = 7.5 × 10–14 cm3 s–1 with known thermochemical data gives the rate coefficient k3(T) [cm3 s–1] ≈ 2 × 10–12 exp(−1937/T), which is able both to reproduce the {NH(v = 0)} values measured in the present N2/H2 MW plasma and to reinterpret the fast discharge flow data (38) with k3(295 K) = 2.8 × 10–15 cm3 s–1.
Having resolved the issue of the primary sources of N and NH species, we are now able to describe further interconversions between the N-containing species. N and NH formed in the plasma region, mainly via reaction 3, participate in fast H-shifting reactions(6)resulting in populations of NH2 and NH3. The family of reactions 6, with rates that depend on the local [H], [H2] and gas temperature T(r, z), along with NHx transport mainly by diffusional and thermodiffusional transfer between hot and cold regions, determine the complex equilibrium between the various NHx species throughout the entire reactor.
In addition, the global balance of N-containing species is determined by the input flow F(N2) and outflow from the reactor (wherein [N2] is still very much greater than the sum of the concentrations of all other N-containing species, including NH3), and the slow interconversion between NHx and N2Hx species. As discussed above, N2Hx → 2NHy conversion is mainly via reaction 3 and, to a lesser extent, reaction 1. The reverse conversion is determined by the reaction(7)with additional contributions from many (generally poorly determined) two-body recombination reactions(8a)(8b)where w = (x + y) – z, as well as the analogous three-body recombinations(9)
Among these, the reactions N + NH2 ↔ N2 + 2H and 2NH ↔ N2 + 2H are the most important under the conditions of the present study. Heterogeneous recombination reactions of NHx species at the metal reactor walls and/or the hot quartz window are also possible, but seemingly unimportant for N2/H2 mixtures. This is, however, in marked contrast to the case with NH3/H2 mixtures, as discussed below.
The above-mentioned processes have obvious parallels with those reported previously (10, 16) for carbonaceous species in MW-activated C/H plasmas, wherein C2H2 is the dominant C-containing species in the hot plasma region irrespective of the choice of carbon source gas, and {CH} was shown both experimentally and theoretically to scale as X0(C)0.5, where X0(C) is the input carbon atom mole fraction. Here, N2 is the dominant N-containing species, and we can undertake a similar analysis of the production and loss rates for the NHx species in the hot plasma region per reactions 1, 3, and 79. The resulting overall balance of N1 species can be written as(10)where [N1] = ∑[NHx] (x = 0–3), and the proportionality coefficients b are independent of X0(N) in the process gas. The terms on the left-hand side represent N1 loss processes, namely, through diffusion out of the hot region of the plasma (with relative rate bdiff,plasma) and reaction (breac) according to any of reactions 79, while the terms on the right represent sources, i.e., the dissociation reactions 1 and 3, respectively. This illustrative balance can be used to obtain the functional dependence of {NHx} on X0(N), and for the NH radical, which is concentrated in the hot plasma core, eq 10 predicts {NH} ∼ X0(N)a. The exponent a may lie between 0.5, in the case that reactions 79 are the dominant NH loss processes, and 1.0, if NHx loss is instead dominated by axial diffusion from the hot plasma core to colder regions near the quartz window and the reactor base plate. The 2-D model predicts a near-linear relationship between {NH} and X0(N), implying that diffusion should dominate, whereas the CRDS and OES measurements are best described by intermediate exponents, as shown in Figure 4a, where a = 0.70, and Figure 7, which has a = 0.81.
The foregoing analysis identifies the hot plasma as the main source of NHx (x = 0–3) species in a MWCVD process employing a N2/H2 gas mixture, and the spatial distributions of the N2, NH3, N, and NH mole fractions returned by the 2-D model, shown in the form of (r, z) maps in Figure 10, are all consistent with production of N1 species in the plasma core and their subsequent diffusion out to the cooler regions. (The spatial distribution of the NH2 mole fraction closely resembles that for NH, and is therefore not shown.) N2 molecules, in contrast, diffuse into the plasma region, where they decompose via reactions 1 and 3. Figure 11 shows net production rates for selected species, including NHx (x = 0–3), calculated at r = 0 as a function of z (i.e., vertical distance above the center of the substrate). The local maxima and minima at z ≈ 19 mm are due to a boundary volume characterized by extensive recombination of ions and electrons diffusing away from the plasma, but without any compensating ionization because of the declining electric field in this region. The N data illustrates much of the complex reactivity: the calculations reveal net production of N atoms in the hot plasma region (z ≈ 12 mm) through reactions 1 and 3, net loss at smaller z due to re-equilibration into the various N1 species, and net production again as z → 0, reflecting the temperature dependence of both the equilibrium constants for the various H-shifting reactions 6 and the local [H]/[H2] ratio. Numerical experiments confirm that the conversion and transport of N-containing species described in this section will be (at most) only weakly perturbed by surface-mediated heterogeneous reactions of NHx species, in marked contrast to the case of MW activated NH3/H2 mixtures, which we now consider.

Figure 10

Figure 10. Two-dimensional (r, z) plots showing the mole fractions of N2, NH3, N, and NH in a 1.2% N2/H2 gas mixture with P = 1.5 kW, p = 150 Torr, and reactor dimensions as defined in the caption to Figure 9.

Figure 11

Figure 11. Net production (i.e., production–loss) rates of selected species plotted as a function of z in a 1.2% N2/H2 gas mixture, for r = 0, P = 1.5 kW, and p = 150 Torr.

4.1.2 NH3/H2 Mixtures

Two-dimensional modeling of the MW-activated NH3/H2 plasma following the same N/H gas-phase chemistry described above (Table 1) yields more extended NHx spatial distributions (Figure 12), with the positions of maximal mole fraction for each species lying further from the plasma core and more toward the source gas inlets than in the N2/H2 case (Figure 10). Furthermore, the predicted directions of diffusional flux are here species-specific due to the presence of an alternative, and dominant, NHx source term: axial and radial diffusion of NH3 from the near-inlet region to all other parts of the reactor volume. Two terms dominate the N1 species balance within the measurement region (0 < z < 20 mm), namely, NH3 diffusion from the gas inlet region and reactive loss:(11)Equation 11 implies a square-root dependence, i.e., {NH} ∼ X0(N)0.5, which is reproduced in both the 2-D model results and the OES measurements, with the latter being well-described by an exponent a = 0.47. Analysis of the CRDS measurements, however, returns a = 0.36. Such a (close to) cube-root dependence on X0(N) could be realized if NHx loss was dominated by one or more three-body reactions, such asbut the present calculations suggest that any such reaction would need to have an improbably large rate coefficient (k > 10–28 cm6 s–1) to be practically important.

Figure 12

Figure 12. Two-dimensional (r, z) plots showing the mole fractions of N2, NH3, N, and NH in a 1.2% NH3/H2 gas mixture with P = 1.5 kW, p = 150 Torr, and reactor dimensions as defined in the caption to Figure 9.

The global N1 balance for NH3/H2 plasmas constitutes another, and more serious, discrepancy between the calculated and measured {NH(v = 0)} z-profiles. The predicted {NH} values exceed the measured column densities by factors of 2–3 at z < 15 mm, peaking at z ≈ 35 mm, far from the hot plasma core; however, the measured {NH(v = 0)} has maximized by z ≈ 15 mm. Various processes could lead to a reduction in the calculated [N1] at large z: (i) Conversion of N1 species to N2, by adsorption of NHx (x = 0, 1) at the reactor walls and on the hot quartz window, with subsequent gas–surface reactions with NH3 producing gas-phase N2H4–x, finally becoming N2 through a sequence of H-abstractions. Calculations show that such conversions will indeed reduce [N1], but not sufficiently to match the experimental observations given that [NH3] > 1016 cm–3 near the gas inlet far exceeds [N] and [NH]. Consequently, an adequate reduction of [N1] would require NH3 loss at the surface with probability γ > 2 × 10–4, independent of the local N and NH fluxes. Such a large value of γ appears unphysical, however, on the basis of the critical sensitivity of the model results to the properties of the near-inlet region. (ii) Contributions from three-body reactions stabilized by collisions with H2, e.g.orSuch reactions cannot be important in practice, however, as they only give a useful reduction of [N1] if we assume unrealistically large rate coefficients, k > 10–29 cm6 s–1.
The most likely cause of this discrepancy, therefore, is the use of a cylindrically symmetric model geometry to describe the gas inlet scheme of the experimental PACVD reactor. Indeed, a similar situation arose in our previous study of MW-activated CH4/CO2/H2 plasmas. (17) The process gas enters the reactor through two diametrically opposed ports positioned at φ ≈ 45° to the probe axis, whereas the 2-D (r, z) model assumes gas entry at r = 60 mm. As Figure 12 shows, the calculated NH3 mole fraction in a 1.2% NH3/H2 plasma falls rapidly with increasing distance from the inlet, which suggests that, in the experiment, there are two sharply localized near-inlet regions where [NH3] > 1016 cm–3 and which extend <10 mm from the respective inlets. The combined volume of these two regions is far smaller than the cylindrically symmetric approximation of a cloud extending from an inlet ring 2πr ≈ 38 cm in circumference. Acknowledging the sensitivity of the NHx radical densities to the NH3 spatial distribution, we anticipate this difference between the experimental and modeled reactor geometries to be primarily responsible for the observed discrepancies. In contrast, in the N2/H2 mixtures, N2 molecules are so stable and so dominant relative to all other N-containing species that they inevitably adopt a near cylindrically symmetric concentration distribution throughout the reactor volume, so that the calculated N2 distribution (Figure 10) deviates little from that of the experiment, regardless of inlet geometry.
A comparison of calculated (r, z) maps of the N2, NH3, N, and NH mole fractions for an NH3/H2 plasma (Figure 12) and the corresponding z-dependent net production rates at r = 0 (Figure 13) with the corresponding plots for the N2/H2 case (Figures 10 and 11) highlights major differences, both in the regions in which the NHx radicals are initially activated, and in the directions of their respective diffusional fluxes. The relatively weak bonding in NH3, in contrast to that of N2, is illustrated by the net loss of NH3 and production of N seen in Figure 13 at z ≈ 50 mm. In the region 45 > z > 35 mm, T increases, and the equilibria associated with the H-shifting reactions 6 shift in favor of NHx (x > 0). Further increasing T at 35 > z > 25 mm leads again to NH3 loss, the net rate of which reaches a local maximum, with corresponding N2 and N formation, in the warm recombinative region at z ≈ 19 mm. Below this lies the plasma proper, where the rising electron density and significant power absorption contribute to a maximum of T, and therefore of [H]. At still smaller z, T falls and ne further increases, leading to the loss of N and N2 and production of both NH3 and the major ions, N2H+ and NH4+. Very close to the substrate, z < 3 mm, NHx (x > 0) is consumed and N atoms are generated, with the latter constituting the dominant N-containing species in this region. Overall, the present calculations succeed in rationalizing the basic conversions and balance within the N/H plasma-chemical kinetic scheme, and are able to account qualitatively (and, in many cases, quantitatively) for the experimental observations.

Figure 13

Figure 13. Net production (i.e., production–loss) rates of selected species plotted as a function of z in a 1.2% NH3/H2 gas mixture, for r = 0, P = 1.5 kW, and p = 150 Torr.

Table 2 summarizes the calculated concentrations of selected species at the approximate center of the plasma, (r, z) = (0 mm, 8.0 mm), and immediately above the substrate, at (0 mm, 0.5 mm), for both N2/H2 and NH3/H2 mixtures under base conditions. The calculated concentrations of the various NHx (0 ≤ x ≤ 2) species are similar in the hot plasma core, but among this family, N is predicted to be dominant close to the substrate. The calculations also predict only modest (less than a factor of 2) differences in these species concentrations in the N2/H2 and NH3/H2 plasmas. We note, however, that X0(N) in the modeled NH3/H2 plasma is only half that used in the N2/H2 plasma modeling.
Table 2. Calculated Concentrations (in cm–3) of Selected Species at Positions (r, z) = (0 mm, 8.0 mm) and (0 mm, 0.5 mm) in N2/H2 and NH3/H2 Plasmas Operating under Base Conditions
mixture1.2% N2 in H21.2% NH3 in H2
z/mm8.00.58.00.5
T /K2799135428211364
H24.85 × 10171.06 × 10184.81 × 10171.05 × 1018
N21.54 × 10155.51 × 10157.48 × 10142.68 × 1015
e2.09 × 10116.76 × 10102.22 × 10117.52 × 1010
H(n = 1)3.09 × 10167.50 × 10153.19 × 10167.83 × 1015
H(n = 2)7.05 × 1071.97 × 1068.39 × 1072.49 × 106
H(n = 3)7.21 × 1061.47 × 1058.72 × 1061.89 × 105
N2(A3)4.79 × 1097.66 × 1092.53 × 1094.26 × 109
N2H5.58 × 1081.94 × 1073.14 × 1084.22 × 107
N2H22.03 × 1066.07 × 1065.46 × 1061.33 × 107
NH31.58 × 10128.94 × 10122.63 × 10121.28 × 1013
NH23.75 × 10111.12 × 10116.53 × 10111.70 × 1011
NH2.87 × 10111.11 × 10115.11 × 10111.71 × 1011
N3.20 × 10111.35 × 10125.74 × 10112.04 × 1012
H2+4.79 × 1053.33 × 1045.74 × 1054.24 × 104
H3+2.69 × 1088.36 × 1066.62 × 1082.34 × 107
N2H+1.13 × 10112.46 × 10109.32 × 10102.06 × 1010
NH4+9.52 × 10104.30 × 10101.28 × 10115.45 × 1010

4.2 Variations with Applied MW Power and Total Gas Pressure

The calculated EEDF is primarily determined by the reduced electric field (E/N), and does not vary with pressure p at constant E/N. (10) Here, we use the previously derived functional form of the absorbed power density, eq 12, to understand the possible changes in plasma parameters and the plasma volume Vpl, with changes in p. (10, 36) That is(12)where the input power P = ∫Q·dVpl. Here, the power density Q has units of W cm–3, E/N is in Townsend units (1 Td = 10–17 V cm2), p is in Torr, and ne is in cm–3. The coefficient C ≈ 0.25 is essentially constant for the present H2-rich plasmas.

4.2.1 Power Dependences

Two-dimensional model calculations for the 1.2% N2/H2 mixture under base conditions and P = 0.8 kW suggest that the measured changes upon increasing P from 0.8 to 1.5 kW are largely explicable by taking VplP, per eq 12, while ne ≈ 2.2 × 1011 cm–3 and Te ≈ 1.24 eV at the plasma center both remain essentially constant. The calculated maximum gas temperature, Tmax, increases by ≈4%, from 2770 to 2890 K, as a result of this increase in P. These increases in Tmax and Vpl are predicted to cause a 3-fold increase in total [H] within the entire reactor volume and a more than 2-fold increase in maximal [H], in good accord with the observed increases in {H(n = 2)} when using both dilute N2/H2 and NH3/H2 source gas mixtures (as shown in Figure 5a).
This increase in [H] elicits a more than 4-fold increase in the calculated {NH(v = 0)}, consistent with the measured increases in both {NH(v = 0)} and the NH* emission intensities from the N2/H2 plasma, as shown in Figures 5a and 8a. The N2 concentration is barely affected by these changes in [H]; the 2-D modeling predicts a modest increase in N2* emission intensity over the range 0.8 ≤ P ≤ 1.5 kW, in accord with experimental observation (see Figure 8a), as a result of the increasing N2(C ← X) EI excitation rate.
In the case of the NH3/H2 plasma, however, this same increase in P causes a modest decrease in {NH(v = 0)}, a smooth increase in the N2* emission intensity, and no clear change in NH* emission. As noted earlier, the predicted {NH(v = 0)} values with the NH3/H2 plasma far exceed those observed experimentally, but the present modeling succeeds (qualitatively at least) in reproducing the observed decrease in {NH(v = 0)}. This is attributable to the order of magnitude decrease in [NH3], particularly in the hot plasma region, as a result of a 3-fold (over the entire reactor volume) increase in [H], which promotes the conversion of NHx to N2.

4.2.2 Pressure Dependences

As eq 12 shows, decreasing p at constant P could be accommodated by (i) a compensating change in Vpl (i.e., Vpl ∼ 1/p), with no effect on E/N, T, or ne; (ii) Vpl remaining constant with increasing E/N and ne; or (iii) a combination of both effects. Inspecting the model outputs for the 1.2% N2/H2 mixture under base conditions and at p = 80 Torr suggests that scenario (iii) is most applicable. Reducing p from 150 to 80 Torr is predicted to result in a ≈35% increase in Vpl (from ≈74 to ≈100 cm3), with corresponding increases of ≈30% in the maximal ne (from 2.2 × 1011 to 2.8 × 1011 cm–3) and ≈10% in Te (from 1.24 to 1.36 eV) at the plasma center. The maximal value of X(H) is reduced by ≈45%, from 7.3% to 4.0%, reflecting the ∼[H2]2 dependence of the thermal dissociation source term.
The present modeling of the N2/H2 plasma captures the observed increases in {H(n = 2)} and {NH(v = 0)} upon increasing p, as depicted in Figure 5b. The calculated z-dependent {NH(v = 0)} profile at lower p is also flatter, in accord with the CRDS measurements (not shown). The model also provides a rationale for the very different p dependences of the N2* and NH* emission intensities displayed in Figure 8b. These intensities are sensitive to the N2(C ← X) and NH(A ← X) EI excitation rates. The former, for example, is given by the product ke(N2(C–X)) × ne × [N2(X)], where the EI rate coefficient for N2(C ← X) excitation is derived from the calculated EEDF, ke = 2.1 × 10–8 × exp(−11/Te[eV]) ≈ 3 × 10–12 cm3 s–1 for a typical value of Te = 1.25 eV. The N2* versus p trend displayed in Figure 8b shows that the net effect of the decreases in ne, Te (and thus ke) with increasing p more than outweigh the (linear) increase in [N2(X)]. The NH(A ← X) EI excitation frequency ke(NH(A–X)) × ne will also decline with increasing p, but the NH* emission is seen to increase and then plateau at p ≈ 150 Torr. This reflects the previously noted greater than linear increase of [NH(X)] (and other NHx species) due to the near quadratic dependence of X(H) with p in the hot plasma region.
The foregoing discussion excludes any possible contribution to the observed N2* emissions from EI pumping of molecules in any state other than the ground state on number density grounds; ke(N2(C ← A3)) is estimated to be an order of magnitude larger than ke(N2(C ← X)), but this difference is overwhelmed by the concentration difference ([N2(A3)]/[N2(X)] < 10–5) in the hot plasma region. The N2(C ← X) excitation must be balanced by N2(C → B) radiative decay and collisional quenching. Probe calculations suggest that the latter must dominate in order to reproduce the observed smooth spatial N2* emission profiles. The only feasible quencher (on concentration grounds) is H2, for which Pancheshnyi et al. (41) report a suitably large N2(C3Πu) + H2 quenching rate coefficient kq > 3 × 10–10 cm3 s–1 (at 295 K).
Notwithstanding the previously noted limited agreement between the experimental data and model outputs for the MW activated NH3/H2 gas mixtures, the 2-D model also succeeds in reproducing the near independence of {NH(v = 0)} with p (Figure 5b), reflecting the alternative NHx source term when using NH3 as the nitrogen source gas, and accounts for the p-dependent N2* and NH* emission intensities shown in Figure 8b. The observed p-dependence of N2* is very similar to that seen with the N2/H2 plasma, for the same reasons. The NH* emission from the NH3/H2 plasma, in contrast, declines with increasing p, which is as expected for the product of a (nearly p-independent) NH(X) density and an NH(A ← X) EI excitation rate coefficient that declines with increasing p.

5 Summary and Conclusions

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Small additions of N2 to MW-activated CH4/H2 gas mixtures used in diamond CVD have been shown to enhance the material growth rate and influence the surface morphology, (2-6) but a complete mechanistic explanation for such behavior has yet to be determined. Here, we have addressed dilute N2/H2 and NH3/H2 microwave plasmas operating under CVD-relevant regimes of gas temperature and pressure, which have otherwise received little attention thus far. The present work can therefore be considered a prerequisite for any subsequent study of N-containing CH4/H2 plasmas, such as those that are used in many diamond CVD reactors. Our investigation has involved three main aspects: (i) CRDS measurements, yielding spatially resolved absolute column densities of H(n = 2) atoms and NH(X) radicals, as functions of gas pressure p, input power P, and mole fraction of nitrogen in the source gas X0(N), (ii) OES measurements of the relative densities of H(n = 3) atoms, NH(A) radicals, and triplet N2 molecules, with respect to the same process conditions; and (iii) complementary 2-D (r, z) coupled kinetic and transport modeling for the same process conditions, including consideration of variations in both the plasma parameters (e.g., Te, T, ne, and power density Q) and the overall chemistry.
Comparisons between experimental measurements and model outputs have provided refinements to the prior understanding of N/H plasma-chemical reactivity, with the proposed scheme now able to demonstrate the interconversion between NHx (x = 0–3) and N2Hx (x = 0–4) species, and its dependence on process conditions and location within the reactor. We have highlighted the essential role of metastable N2(A3Σ+u) molecules (formed by electron impact), and their hitherto underappreciated reactivity with H atoms, in converting the N2 process gas into reactive NHx (x = 0–3) radical species. We have also illustrated the much more extensive NHx spatial distributions prevailing in MW-activated NH3/H2 plasmas, and the importance of surface-mediated NHx loss processes in establishing the measured radical densities in the case of the NH3 feedstock. The overall result is that we are now satisfactorily able to rationalize the observation that measured NH column densities differ by less than a factor of 2 between N2/H2- and NH3/H2-based MWPACVD processes operating under base conditions with the same nitrogen atom input mole fraction, though the difference is larger at lower p and/or P. An important additional finding in the CVD context is that N atoms are, by an order of magnitude, the dominant reactive nitrogenous species in the near-substrate region under the present conditions.

Author Information

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  • Corresponding Authors
    • Michael N. R. Ashfold - School of Chemistry, University of Bristol, Bristol, BS8 1TS United Kingdom Email: [email protected]
    • Yuri A. Mankelevich - Skobel’tsyn Institute of Nuclear Physics, Moscow State University, Leninskie gory, Moscow 119991, RussiaInstitute of Applied Physics, (IAP RAS), 46 Ulyanov st., 603950 Nizhny Novgorod, Russia Email: [email protected]
  • Authors
    • Benjamin S. Truscott - School of Chemistry, University of Bristol, Bristol, BS8 1TS United Kingdom
    • Mark W. Kelly - School of Chemistry, University of Bristol, Bristol, BS8 1TS United Kingdom
    • Katie J. Potter - School of Chemistry, University of Bristol, Bristol, BS8 1TS United Kingdom
    • Mack Johnson - School of Chemistry, University of Bristol, Bristol, BS8 1TS United Kingdom
  • Notes
    The authors declare no competing financial interest.

Acknowledgment

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The Bristol authors gratefully acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC, Grants EP/H043292/1 and EP/K018388/1) and Element Six Ltd., and the many and varied contributions from colleagues Dr. C. M. Western, Dr. J. A. Smith, and K. N. Rosser. Yu.A.M. is grateful to Act 220 of the Russian Government (Agreement No. 14.B25.31.0021 with the host organization IAPRAS).

Appendix

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The earlier fast discharge flow studies of reactive conversions in N2(A3)/H2/Ar and N2(A3)/H/H2/Ar gas mixtures involved monitoring relative (and, with appropriate calibration experiments in many cases absolute) H atom, N2(A3) molecule and NH(X) and NH2(X) radical concentrations downstream of the mixing region. (38) Data relevant to the current study have been simulated using the following minimalist reaction scheme (with respective rate coefficients kAi (cm3 s–1) at the experimental temperature T = 295 K):(A1)(A2)(A3)(A4)
These rate coefficients were drawn from various sources: kA1 and kA2 from experimental data surveyed in the Herron evaluation, (39)kA4 from the combined experimental and theoretical study of reaction A4 by Adam et al., (42) and kA3 derived from present study. This value of kA3 does not contradict the conclusion of the Ho and Golde study, (43) given it is so much smaller than kA2 (kA3 ≈ 1.3 × 10–5 × kA2). The simple mechanism (A1)–(A4) is able to replicate many of the features observed in the fast discharge flow experiments, e.g., the lack of any discernible increase in [NH] at the measurement time, t = 14 ms, upon introducing H atoms at a concentration [H] = 1.1 × 1014 cm–3 (X(H) = 0.17%). The fact that the observations are made downstream, after a user-selected time delay t, is crucial to the interpretation. As Figure 14 shows, reaction A3 leads to an initial increase in [NH], which has then declined precipitously by the time of the measurement through reaction A4 with the high concentration of H atoms.
Though appealing, this simple analysis of the prior data may well be deficient in detail. For example, we note that the present calculations return [H] concentrations in the experiments using the 0.001% N2(A3)/25% N2/2.3% H2/Ar gas mixture (i.e., without any deliberate H atom addition, Figure 14a) that are an order of magnitude larger than the measured value ([H] ∼ 1010 cm–3, per ref 38). Such a low [H] is inconsistent with the kA1 value assumed here and in ref 38, but we recognize that the experimental [H] values could be underestimated as a result of, for example, H atom recombination on the Pyrex tube surface.

Figure 14

Figure 14. Evolution of selected species concentrations in the fast discharge flow experiments assuming the simple reaction scheme A1A4 for a 0.001% N2(A3)/25% N2/2.3% H2/Ar mixture (a) without and (b) with the addition of atomic hydrogen at a mole fraction X(H) = 0.17%.

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The Journal of Physical Chemistry A

Cite this: J. Phys. Chem. A 2015, 119, 52, 12962–12976
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Published November 23, 2015

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  • Abstract

    Figure 1

    Figure 1. Part of the NH(A–X) Δv = 0 band system (a) as measured by CRDS at z = 8 mm in a N2/H2 (6/500 sccm) plasma operating under base conditions, with fitted PGOPHER simulation at fixed Trot = Tvib = 2900 K, and (b) shown in the context of the complete (simulated) progression, illustrating the overlapping v′–v″ = 0–0, 1–1, and 2–2 bands.

    Figure 2

    Figure 2. Optical emission spectra, measured at z = 7 mm, of a MW-activated N2/H2 (9/500 sccm) mixture operating otherwise under base conditions. (a) Overview spectrum showing the NH(A–X) Δv = 0 band system centered at ≈336 nm, along with three progressions of bands from the second positive (C3Πu–B3Πg) system of N2. Panel (b) shows an expanded view of the N2(C–B) Δv = −1 and Δv = −2 progressions, while part (c) illustrates the overlapping N2(C–B) 0–0 band and NH(A–X) Δv = 0 progression. Both are shown together with a common PGOPHER simulation, vertically offset for clarity in part (b), using the appropriate spectroscopic constants and with respective rotational temperatures treated as parameters and varied for best fit.

    Figure 3

    Figure 3. Profiles of {NH(v = 0)} (black circles) and {H(n = 2)} (red triangles) with respect to z obtained by CRDS probing of (a) N2/H2 (6/500 sccm, filled symbols) and (b) NH3/H2 (6/500 sccm, open symbols) plasmas operating under base conditions. The gray and orange lines are calculated {NH(v = 0)} and {H(n = 2)} profiles, respectively.

    Figure 4

    Figure 4. Variations in {H(n = 2)} and {NH(v = 0)} for (a) N2/H2 and (b) NH3/H2 plasmas plotted as a function of N/H ratio in the input gas mixture (defined on the top and bottom horizontal axes, respectively). Both plasmas operated otherwise at base conditions and were probed at z = 8 mm. The symbol key is as in Figure 3. The black lines are curves of the form {NH(v = 0)} ∼ X0(N)a, with best-fitting exponents of (a) a = 0.70 and (b) a = 0.36. The gray squares and orange diamonds show calculated values of {NH(v = 0)} and {H(n = 2)}, respectively, under the given conditions. The calculated {NH(v = 0)} values for the NH3/H2 plasma (not shown) are roughly twice the experimental values, as discussed in the text.

    Figure 5

    Figure 5. Variations in {H(n = 2)} and {NH(v = 0)}, probed at z = 8 mm, with respect to (a) applied MW power and (b) pressure. The plasmas were maintained otherwise at base conditions, with flows of 6/500 sccm for both the N2/H2 and NH3/H2 mixtures. The symbol key is as in Figure 4, with filled and open symbols for the N2/H2 and NH3/H2 plasmas, respectively. Points in each series are joined by straight line segments for visual clarity. Calculated {H(n = 2)) and {NH(v = 0)} values are again indicated with orange diamonds and gray squares, respectively, and the latter values for the NH3/H2 plasma are off scale and thus not shown.

    Figure 6

    Figure 6. z-profiles of H*, NH*, and N2* emissions from (a) N2/H2 (3/500 sccm) and (b) NH3/H2 (6/500 sccm) plasmas, both operating under base conditions. The emission intensities displayed in both panels are mutually normalized, for each species, to the maximal value measured at any z from either plasma. The symbol key is as in the previous figures, with the addition of blue diamonds for N2*. The orange lines show calculated H(n = 3) (relative) concentrations at r = 0 as a function of z for the respective plasmas, and match well with the measured H* emission profiles. The points in the NH* and N2* profiles are joined with straight line segments for visual clarity.

    Figure 7

    Figure 7. H*, NH*, and N2* emission intensities measured at z = 7 mm for N2/H2 (filled symbols) and NH3/H2 (open symbols) plasmas, both operating under otherwise base conditions, plotted as a function of N/H ratio in the input gas mixture. Symbols are as in Figure 6. Emission intensities are normalized to the maximum value observed for each species, and flow rates of the respective nitrogen precursors are expressed as N/H atom ratios. The black lines are curves of the form NH* ∼ X0(N)a, with best-fitting exponents of a = 0.81 in the N2/H2 case and a = 0.47 for NH3/H2.

    Figure 8

    Figure 8. NH* and N2* emission intensities measured (a) at z = 7 mm (N2/H2 plasma, 3/500 sccm, filled symbols) and z = 5 mm (NH3/H2 plasma, 6/500 sccm, open symbols) as a function of P and (b) at z = 5 mm for N2/H2 (3/500 sccm) and NH3/H2 (6/500 sccm) plasmas (filled and open symbols, respectively) as a function of p. All other parameters were maintained at their base values, and the emission intensities for each species are mutually normalized to the maximal value measured at any P, in panel (a), or p, in panel (b), from either plasma. Calculated values of the (relative) N2(C ← X) and NH(A ← X) EI excitation rates are shown as pale blue triangles and gray squares, respectively.

    Figure 9

    Figure 9. Two-dimensional (r, z) distributions of gas temperature T and electron concentration ne for base conditions and 1.2% N2/H2 mixture. The model assumes cylindrical symmetry, a substrate diameter of 3 cm, and a reactor radius, Rr = 6 cm, and height, h = 6.2 cm.

    Figure 10

    Figure 10. Two-dimensional (r, z) plots showing the mole fractions of N2, NH3, N, and NH in a 1.2% N2/H2 gas mixture with P = 1.5 kW, p = 150 Torr, and reactor dimensions as defined in the caption to Figure 9.

    Figure 11

    Figure 11. Net production (i.e., production–loss) rates of selected species plotted as a function of z in a 1.2% N2/H2 gas mixture, for r = 0, P = 1.5 kW, and p = 150 Torr.

    Figure 12

    Figure 12. Two-dimensional (r, z) plots showing the mole fractions of N2, NH3, N, and NH in a 1.2% NH3/H2 gas mixture with P = 1.5 kW, p = 150 Torr, and reactor dimensions as defined in the caption to Figure 9.

    Figure 13

    Figure 13. Net production (i.e., production–loss) rates of selected species plotted as a function of z in a 1.2% NH3/H2 gas mixture, for r = 0, P = 1.5 kW, and p = 150 Torr.

    Figure 14

    Figure 14. Evolution of selected species concentrations in the fast discharge flow experiments assuming the simple reaction scheme A1A4 for a 0.001% N2(A3)/25% N2/2.3% H2/Ar mixture (a) without and (b) with the addition of atomic hydrogen at a mole fraction X(H) = 0.17%.

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